Question: Sean tried to drink a slushy as fast as he could. He drank the slushy at a constant rate. There were originally $275$ milliliters of slushy in the cup. After $13$ seconds, $210$ milliliters of slushy remained. How fast did Sean drink?
Let's say that Sean drinks $V$ milliliters of slushy per second. Then, he drinks $V\cdot T$ milliliters in $T$ seconds. In addition, we know that there were originally $275$ milliliters of slushy in the cup. The remaining amount of slushy is found by taking the original amount and subtracting from it the amount Sean had already drunk. We can express this with the equation $R=275-V\cdot T$, where: $R$ represents the remaining amount of slushy to drink at a given time (in milliliters) $V$ represents Sean's drinking speed (in milliliters per second) $T$ represents the time (in seconds) We know that after $13$ seconds $(T={13})$, $210$ milliliters of slushy remained $(R={210})$. Let's plug these values into the equation to find the value of $V$. $ \begin{aligned}{210}&=275-V\cdot{13}\\ 13V&=65\\ V&=5\end{aligned}$ Therefore, Sean drank at a rate of $5$ milliliters per second. To find how long it took Sean to drink all the slushy, we can plug $R=0$ into the equation and solve for $T$. $ \begin{aligned}0&=275-5T\\ 5T&=275\\ T&=55\end{aligned}$ Sean drank at a rate of $5$ milliliters per second. It took Sean $55$ seconds to drink all the slushy.